New Mars Forums

Can I assume that you're referring to my post on finding a limit to CO2 tolerance? If so, I can provide you references to the 40+ peer-reviewed papers that I researched when coming up with the 120 mbar value. As an example, the papers came from such publications as The American College of Chest Physicians, The Journal of Applied Physiology, European Neurology, The American Society for Clinical Investigation, The American Physiological Society, Aerospace Medicine, and many other reputable sources.

You are absolutely correct in questioning source veracity, and I would be happy to answer any concerns you have over my estimate, if I am correct in interpreting that is the issue at hand.

I'm making this (admittedly massive) post in an attempt to correct some stuff I've seen on these forums and offer some new information about the requirements for a breathable atmosphere. The overall goal is to present an upper limit to tolerable CO2 levels (jump to the end if you just want to know), but I'd like to start with two general points:

*************************************************************

Saying that humans can't live with more than [insert safety data sheet value] mbar of CO2 because of tocixity is like saying people can't live in the Andes because of lack of O2.
Occupational Safety and Health Administration guidelines dictate that the Permissible Exposure Limit for CO2 is 0.5%, and the level Immediately Dangerous to Life and Health is 5% (both assume a total pressure of 1 atm, i.e. sea level). At these levels shortness of breath, headache, and dizziness are reported. Similar symptoms are associated with altitude sickness, which begins to occur when someone from sea level ventures up to altitudes of 1500-3500 m. Contrast this with the fact that the city of Potosi in Bolivia is located at 4000 m and has a population of over 130,000 according to the INE 2001 census. The point is that the acclimation capabilities of humans (and other organisms) should not be underestimated.
Sources:
High Altitude Illness, Ivan Schatz, M.D., Western University of Health Sciences
www.californiamountaineer.com/HIGH%20ALTITUDE%20ILLNESS.pdf
Ansul Incorporated Carbon Dioxide Material Safety Sheet
www.ansul.com/AnsulGetDoc.asp?FileID=13400

Breathing 5% CO2 on Earth is not the same as breathing 5% CO2 on Mars.
This is a common misconception I've noticed on these forums, and it really needs to be cleared up. The truth is that respiration in organisms depends only on partial pressure of gases. Going by just percentages will get you in trouble. Let's do an example. Say that Bob has acclimated to breathing 5% CO2 on Earth at sea level. What this really means is that he has acclimated to breathing (5% CO2)*(1 atm total) = 50 mbar CO2. Now let's put him in a terraformed Mars atmosphere of 250 mbar. The amount of CO2 Bob can handle on Mars is the same as on Earth: 50 mbar CO2. But when you convert to percentages, that's (50 mbar CO2)/(250 mbar total) = 20% CO2. I hope this simple example gets the point across that taking straight gas percentages can be inaccurate when considering the breathability of a terraformed Martian atmospshere.

*************************************************************

So, how much CO2 can we take? Here are the key effects to consider:

#1) CO2 replaces O2 on hemoglobin, thus depriving you of oxygen
#2) CO2 causes acidosis, i.e. a blood pH imbalance
#3) CO2 causes an inert gas narcosis, similar to nitrogen in scuba diving

#1: INHIBITION OF O2-HEMOGLOBIN BONDING

The first effect, inhibition of O2-hemoglobin bonding, turns out to be negligible:

Only a small fraction of the CO2 in your blood is transported by hemoglobin.
The vast majority (~90%) of the CO2 in blood is transported by bicarbonates.
Source: Clinical Anesthesiology, M. J. Murray, G. E. Morgan, and M. S. Mikhail, New York: McGraw-Hill (2002)
http://books.google.com/books?id=Z8BFSS9tsgwC

Blood CO2 levels have only a small effect on O2 binding to hemoglobin.
To illustrate: Like elevated CO2 levels, raising body temperature negatively impacts O2-hemoglobin binding. Normal CO2 arterial pressure is 40 mmHg. Increasing this over seven times to 300 mmHg (400 mbar) has as much effect on O2-hemoglobin binding as raising core body temperature to 102.6°F, which is only a moderate fever. Fevers aren't fun, but no one dies from respiratory failure due to inadequate O2-hemoglobin bonding.
For more information, play with this applet: http://www.ventworld.com/resources/oxyd … disso.html

#2: RESPIRATORY ACIDOSIS

The second effect, acidosis, is the major cause of the toxicity typically associated with CO2. But what seems not to be so widely known is that it can be overcome through acclimation over a few days, much like altitude sickness. As I've noted in a previous post, this is because the carbonic acid formed in the blood by the CO2 is neutralized by the kidneys retaining bicarbonates ions. Just to reiterate, humans have been adapted without significant complications to 4% CO2, Rhesus monkeys to 6% CO2, and sheep to 12% CO2.

Only in the experiment with sheep was some sort of limit of acclimation reached. The study was reported on in at least two papers from the early 70s by Hoover et al., who detailed the nutritional and physiological responses. Negative effects began around 8% CO2, but were tolerable up till 12% CO2. Eventually serious degradation occured at 16% CO2, with the sheep becoming lethargic, beginning to drool, and ceasing to eat. Subsequently, the experiment was stopped. But the question is, what caused these symptoms? There does not seem to be any obvious reason why the bicarbonate buffer of the body would fail at that level.

#3: INERT GAS NARCOSIS

The answer is that the third effect, inert gas narcosis, is coming into play. It turns out that every gas has some pressure at which breathing it will cause symptoms similar to being drunk. At even higher pressures it will act as an anesthetic. These effects are thought to be due to the gas diffusing across cell membranes and interfering with neural signals. Thus, the narcotic potency of a gas would be expected to be related to its solubility in lipids and oils. This is confirmed by experiment. The graph below depicts the points at which a number of gases cause inability to feel pain in a standardized test:

So chloroform is a good anesthetic because it is extremely oil soluble and will knock you out at only trace pressures, while helium is almost impossible to "overdose" on in terms of narcotic effects and is thus used in deep diving where you have to breathe high pressure gases. Nitrogen isn't quite as good as helium, and so its narcotic effects can be significant when diving at relatively shallow depths. For nitrogen a biological response, not significantly impairing, can occur as shallow as 60 ft of sea water, or 1.5 atm of pressure, which for breathing air would be 1.2 atm N2. The safety guideline limit is 100 ft of sea water, or about 2.4 atm N2. Deeper than this and serious impairment of judgement similar to drunkeness can occur.

Now look at where carbon dioxide is on the graph. It's much more narcotic than one would expect based on the lipid solubility theory. This increased potency is due to acidosis, the second biological effect of CO2 on our list. But we know that the effects of acidosis can be compensated for by the kidneys. This means that, given time to acclimate, the narcotic potency of CO2 will decrease, and it will move up on the graph to join the company of nitrous oxide (laughing gas) and xenon. Thus, the theory of inert gas narcosis provides us with the real limit to breathable CO2 levels.

So what exactly is this limit? According to lipid solubility theory CO2 should be 20 times more potent than N2. This suggests that biological response will begin at about (1.4 atm N2)/20 = 70 mbar CO2, or 7% CO2 at sea level, and the safety limit will be (2.4 atm N2)/20 = 120 mbar CO2, or 12% CO2 at sea level. I was quite happy when I saw this, because it agrees well with the study on sheep that I mentioned before.

Now I want to note that there's significant "wiggle room" in these calculations. For example, it is difficult to evaluate the narcotic contribution of O2 at high pressure when looking at diving, but some people think that it's similar to N2. If we accept that and redo the calculations, we find a biological reaction threshold of about 90 mbar CO2 (9% CO2) and a safe limit of 150 mbar (15% CO2). These are a bit different from the numbers we got assuming just N2 was narcotic, but they're still consistent with the sheep experiment. Also, while it's true that sheep and humans have similar inert gas narcosis reactions, it turns out that humans are 8% more "durable", i.e. the sheep study pressures have to be bumped up 8% to get a correct pressure/response correlation for humans. Finally, and perhaps more intriguing, it seems that there may actually be the possibility of acclimation to inert gas narcosis. Some frequent divers are capable of operating safely at depths down to 180-220 ft, which, depending on whether you try to include O2 narcosis or not, is equivalent to between 220-340 mbar CO2, or 22-34% CO2 at sea level. This is somewhat speculative though.

Ultimately, we can state with confidence a conservative lower estimate of 120 mbar for the limit of safe CO2 partial pressure. This raises the possibility that CO2 might actually be used as a significant buffer gas in terraformation.

References:

Extreme Hypercapnia in Humans

A case of extreme hypercapnia (Urwin et al. 2004)
Extreme Hypercapnia in a Fully Alert Patient (Meissner & Franklin 1992)

Effects of Hypercapnia

Bone Loss in Patients with Untreated Chronic Obstructive Pulmonary Disease Is Associated with Hypercapnia (Dimai et al. 2001)
Structural basis of hypoxic pulmonary hypertension; the modifying effect of chronic hypercapnia (Howell et al. 2004)
Circadian pattern of ventilation during acute and chronic hypercapnia in conscious adult rats (Seifert & Mortola 2002)
Hypercapnia Does Not Affect Functional Residual Capacity Enlargement Induced by Chronic Hypoxia (Maxova & Vizek 2002)
A Pharmacologic Study on CO2 Responsiveness of Intracranial Pressure in Rats With Chronic Hypercapnia (Kondo et al. 1999)
Cerebral Blood Flow Autoregulation and Graded Hypercapnia (Raichle and Stone 1971)
Chronic hypercapnia resets CO2 sensitivity of avian intrapulmonary chemoreceptors (Rebout and Hempleman 1999)
Chronic Hypercapnia Stimulates Proximal Bicarbonate Reabsorption in the Rat (Cogan 1984)
Effects of acute and chronic hypercapnia on oxygen tolerance in rats (Clark 1981)
Mechanisms of Adaptation to Chronic Respiratory Acidosis in the Rabbit Proximal Tubule (Krapf 1989)
Size and Composition Changes in Diaphragmatic Fibers in Rats Exposed to Chronic Hypercapnia (Kumagai et al. 2001)
The Effect of Prolonged Experimental Hypereapnia on the Brain (Matakas et al. 1978)
The Influence of Graded Degrees of Chronic Hypercapnia on the Acute Carbon Dioxide Titration Curve (Goldstein et al. 1971)
Ventilatory responses to acute and chronic hypoxic hypercapnia in the ground squirrel (Webb & Milsom 1994)
Ventilatory responses to hypercapnia and hypoxia following chronic hypercapnia in the rat (Kondo et al. 2000)
The brain in extreme respiratory acidosis (Paljärvi et al. 1982)

Effects of Hypercapnia + Hypoxia

Carbon Dioxide-Oxgen Interactions in Extension of Tolerance to Acute Hypoxia (Lambertsen et al. 2001)
Cardioprotective Effect of Chronic Hypoxia is Blunted by Concomitant Hypercapnia (Neckar et al. 2003)
Chronic hypercapnia inhibits hypoxic pulmonary vascular remodeling (Ooi et al. 2000)
Hypercapnia Does Not Affect Functional Residual Capacity Enlargement Induced by Chronic Hypoxia (Maxova et al. 2002)
Renal compensation to chronic hypoxic hypercapnia (de Seigneux et al. 2007)
Respiratory adaptation to chronic hypercapnia in newborn rats (Rezzonico et al. 1989)
Therapeutic hypercapnia prevents chronic hypoxia-induced pulmonary hypertension in the newborn rat (Kantores et al. 2006)
Vascular Changes in the Rat Brain during Chronic Hypoxia in the Presence and Absence of Hypercapnia (Miyamoto et al. 2005)
Ventilatory responses of hamsters and rats to hypoxia and hypercapnia (Walker et al. 1955)
Ventilatory Acclimatization to High Altitude Is Prevented by CO2 Breathing (Cruz et al. 1979)

Inert Gas Narcosis

Effect of habituation to subanesthetic N2 or N2O levels on pressure and anesthesia tolerance (Brauer et al. 1987)
Effects of CO2 and N2 partial pressures on cognitive and psychomotor performance (Fothergill et al. 1991)
Narcotic effects of nitrous oxide and compressed air on memory and auditory perception (Fowler et al. 1980)
"NOAA Diving Manual: Diving for Science and Technology" U.S. Department of Commerce, DIANE Publishing (1994), p 3-20. Section 3.2.3.5 Inert Gas Narcosis
http://books.google.com/books?id=MV55Xe … 0788102311
(I don't know why Google Book Search thinks this is a book on the history of the coal industry in the USA...it isn't)
Effects of epidural and intravenous buprenorphine on halothane minimum alveolar anesthetic concentration and hemodynamic responses (Inagaki & Kuzukawa 1997)
Fetal Anesthetic Requirement (MAC) for Halothane (Gregory et al. 1983)
"Shnider and Levinson's Anesthesia for Obstetrics" Samuel C. Hughes, Gershon Levinson, Mark A. Rosen, Lippincott Williams & Wilkins (2002)

The (Infamous) Sheep Study

Effects of High Carbon Dioxide Levels on Nutrition of Sheep (Knowlton et al.)
Ovine Nutritional Responses to Elevated Ambient Carbon Dioxide (Hoover et al. 1971)
Ovine physiological responses to elevated ambient carbon dioxide (Hoover et al. 1970)

Miscellaneous

Neuronal sensitivity to hyperoxia, hypercapnia, and inert gases at hyperbaric pressures (Dean et al. 2003)
Alveolar-arterial P_CO2, difference during rebreathing in patients with chronic hypercapnia (McEnvoy et al. 1974)
Anthropometric and Other Factors Affecting Respiratory Responses to Carbon Dioxide in New Guineans (Patrick & Cotes 1974)
Negative arterial-mixed expired P_CO2 gradient during acute and chronic hypercapnia (Jennings & Chen 1975)
Summary of Data on Carbon Dioxide (Law firm of Covington & Burling 1986)
The carbon dioxide capacity of the human body (Adolph et al. 1928)
The Effect of Increased Ambient CO2 on Arterial CO2 Tension, CO2 Content and pH in Rainbow Trout (Cameron & Randall)
Tolerance of the Dog Heart to Carbon Dioxide (Brown & Miller 1952)

Websites

The Interactive Oxyhemoglobin Dissociation Curve
http://www.ventworld.com/resources/oxydisso/dissoc.html
Respiratory Acidosis, by Margaret Priestly
http://www.emedicine.com/PED/topic16.htm
Extending The Envelope: A Primer On Self-Contained Diving Technology
http://www.cisatlantic.com/trimix/AQUAc … Diving.htm
SDUA Standard Gas Mixes
http://www.sduadivers.com/resources/200 … gas-mixes/
Exotic Diving Gases
http://www.techdiver.ws/exotic_gases.shtml
Carbon Dioxide, Narcosis, and Diving
http://www.livingseas.com.sg/articles/a … rcosis.htm
Breathing Control in Chronic Hypercapnia
http://www.rtmagazine.com/issues/articl … -06_12.asp

I considered this myself a while back and came to the conclusion that it was a beautiful idea...except for two things:

#1 Both methane/hydrogen are very light molecules that won't get caught in a cold trap. Most/all of their components are hydrogen, so once they get to altitudes where UV is strong they turn into lots of H which happily drifts off into space. Bye-bye, atmosphere!

#2 If the methane/hydrogen level ever drops to flammable levels through negligence/accident there'd automatically be a horrible global holocaust.

The second problem could be avoided if you were really careful, but there's not much you can do about the first, which is why I eventually abandoned the idea.

I found a great paper on arctic plants that can tolerate anoxia in the dark for a week and still be green and ready to photosynthesize afterward. It's titled "Anoxia Tolerance in High Arctic Vegetation" (Crawford et al. 1994). Here are a couple plants from the paper that I could immediately think of uses for:

Poa alpina............................Alpine Meadow-Grass.........possibly bred for grain
Eriophorum scheuchzeri.......White Cottongrass.............textile fibre and bog methane venting
Carex misandra....................Short Leaved Sedge...........marsh methane venting
Juncus biglumis....................Two-Flowered Rush............marsh methane venting

I'd had my eye on cottongrass for a while, but I didn't know it was anoxia tolerant as well until I read this.

These high plants come very close to (and possibly are on par with) lichen and bryophytes in their ability to tolerate low/no oxygen and survive anoxic Martian nights early on in terraformation. They're also a whole lot handier! Many of them contribute to warming the planet by venting methane produced in boggy and marshy ground as a side effect of cellulose breakdown/carbon sequestration.

Ummmm, not exactly.

Yes, natural fires would increase as O2 levels rose on Mars. However, once you get to the point where you're having forest/tundra fires that convert O2 to CO2 at the same rate that the plants are converting CO2 to O2, you've reached a stable equilibrium. What O2/CO2 ratio that'd exactly be is a very complex question.

I took the liberty of crunching the numbers for warming up Pluto to Earth temperature using super-greenhouse gases. I think it is fairly obvious that this would be the easiest known icy dwarf planet to terraform (though that's not saying much). It turns out to be not quite as ridiculous a proposition as one might think, though it is necessary to discard any thoughts of having the GHGs "take the place of Nitrogen".

We assume that we have a thermally grey concoction of GHGs. In order to raise Pluto's average temperature from 50K to an Earth-like 288K would then require enough GHGs to produce a thermal optical thickness of 600. Using fluorinated super GHGs this is equivalent to a molecular column of ~1e25 m^-2 or a surface GHG pressure of ~5 microbar. Dwarf planets further out than Pluto would typically require more GHGs. Compare this to Mars, which would require an optical thickness of 3, a molecular column of 5e22 m^-2, and a surface GHG pressure of 0.1 microbar to produce a similar warming effect. I refer you to "Keeping Mars warm with new super greenhouse gases" (Gerstell et al. 2001) for details.

There is much evidence that the surfaces of Pluto, Triton, and similar trans-Neptunian objects are coated with significant amounts of nitrogen ice. This would be released to form an atmosphere as the body was warmed. Unfortunately, just how much nitrogen ice is on Pluto (or any of these bodies) is very poorly constrained; the current lower and upper limits for average surface thickness are of order 10 cm and 1 km respectively. More info is available in "Seasonal Nitrogen Cycles on Pluto" (Hansen and Paige 1996). If there is about 100 m of nitrogen ice on Pluto a 1000 mbar atmosphere much like that of early Earth would be produced. Significant amounts of ammonia, carbon dioxide, methane, and water vapor might also be present, but these would have small effects on atmospheric pressure and be virtually negligible in terms of contributing to the greenhouse effect already produced by the super GHGs. Due to the high ice content of the planets in question, the system would become a "waterworld" with a rocky core as the body thawed over millenia.

The biggest problem with the whole idea is where to get a large supply of fluorine to produce the super GHGs. The existence of fluorine on icy dwarf planets is pure speculation, and expecting significant amounts is pretty much fantasy. On the order of 1e14 kg of calcium fluoride ore would be needed to initially warm Pluto. At the current global fluorite mining rate on Earth (~5 million metric tons per year) it would take 20 millenia to produce that. Unfortunately, Earth's known fluorite and fluorite equivalent phosphate resources are less than 1e12 kg. You'd need to find 100 times more fluorite, either on Earth where we don't have mines yet or on an extraterrestrial body. On the bright side, once you had built up your initial GHG levels your replacement rate would be very low. This is because UV strength and solar wind density, which dominate super GHG destruction rates, are miniscule at Pluto's orbit.

A problem I'm not sure of the answer to is making the fluorinated super GHGs vaporous when beginning; all of them are solid at Pluto's current temperature. Their vapor pressures may be sufficient to get things rolling, but some initial external heating may be necessary as Austin Stanley suggested.

Not super rare, but rare enough we can't do much but introduce trace global amounts to any significant planet. There's about 540 ppm fluorine in Earth's crustal rocks by weight, and only 89 ppm in carbonaceous meteorites, which you could take as a proxy for asteroids. The Earth's crust (the lithosphere) is about 2% of its total mass, or about 1e23 kg. That means there's only about 5e19 kg of fluorine that's really accessible on Earth. It's a very rough comparison, but contrast that with the mass of Earth's atmosphere, which is about 5e18 kg. This suggests we'd have to mine approximately 10% of the Earth's crust to get enough fluorine for a serious atmosphere. Even mining 1% would be a phenomenal task; it would be like completely dismantling Ceres, previously considered the largest asteroid.

FC4? Do you mean tetracarbon monofluoride? I can't say I know a lot about it, but from what I understand it's a solid under standard conditions.

You scared me for a second, but I'm happy to say my sig's correct. You can read the original article it came from here. It's at the end of the fourth paragraph.

The ability of human beings to breathe and operate effectively in a given atmosphere depends primarily on how much oxygen reaches the alveola in the lungs. When you breathe in air from the atmosphere it is warmed and becomes saturated with water vapor from your internal tissues. Since the pressure in your lungs is (normally) the same as the pressure outside your body, water vapor saturation displaces some of the oxygen in the air you breathed in. The effect of displacement by carbon dioxide diffusing from the bloodstream must also be considered. Quantitatively, we have the Alveolar Gas Equation:

        pAO2 = fO2*(pAtm - pH2O) - paCO2/R

        pAO2 is the alveolar oxygen pressure
        fO2 is the fraction of oxygen in the atmosphere
        pAtm is the atmospheric pressure
        pH20 is the water vapor pressure which at 37°C (body temperature) is 47 mm Hg (63 mbar)
        paCO2 is the arterial pressure of carbon dioxide, which is usually 40 mm Hg (53 mbar) at sea level (it decreases somewhat with altitude)
        R is the "respiratory quotient" which is 0.8 in normal air at sea level, but is 1.0 when on 100% O2 and can be over 1.0 under unusual circumstances. It is a metabolic parameter and equal to (CO2 released)/(O2 absorbed).

The effects of low pressure on human respiration have been studied most in the context of high altitudes. Human beings have lived at 5,100 m (16,730 ft) in a permanent settlement, and they have great difficulty acclimating above 5,500 m (18,040 ft). Above this, the human body begins to experience degradation rather than acclimation. There is documented evidence of people living at 5,950 m (19,520 ft) for 2 years (West, 2002). Above 7,000-8,000 m (25,000-26,000 ft) the human body cannot sleep or carry out digestion and many bodily functions shut down. This is the Death Zone, where acclimation is impossible.

The next paragraph is a bit technical, and for those who want to play with data and numbers themselves.
As noted above, paCO2 can decrease as one acclimatizes to higher altitudes. Some numbers can be found here in Table 3. Although the 5th column says "alveolar CO2", which would be the CO2 pressure in the lungs (paCO2/R), the numbers don't quite work for low altitudes. All the other columns seem to be correct. I am inclined to suspect that the 5th column is actually reporting the "arterial CO2" (paCO2), because then the discrepancy can be taken into account by the metabolic parameter R, which would then be ~0.86 at sea level and increase towards unity as you ascended. R would then exceed unity after entering the Death Zone, which makes some sense since normal metabolic processes are disrupted there. I only mention this if anyone wants to play with the data themselves. All that really matters for our purposes are the pAO2 values in the table, which are correct.

Here are measured and calculated pAO2 for some representative situations:

0 ft (sea level):
Measured pAO2 = 137 mbar

10,000 ft (about the height of Leadville, Colorado):
Measured pAO2 = 81 mbar

18,000 ft (the highest one can fully acclimate, and about Everest Base Camp):
fO2 = 0.21, pAtm = 506 mbar (0.50 atm). For R~1 and pACO2 ~ 40 mbar, we get pAO2 ~ 53 mbar (40 mm Hg), which agrees with interpolation from measured values

20,000 ft (the highest people have lived for extended periods):
measured pAO2 = 45 mbar (34 mm Hg)

25,000 ft (the Death Zone; acclimation impossible and steady degradation of body functions experienced):
measured pAO2 = 40 mbar (30 mm Hg)

RobertDyck's fighter pilots:
fO2 = 1.0, pAtm = 170 mbar (2.5 psi), R = 1.0
for unacclimated pilots (paCO2 = 53 mbar) we get pAO2 ~ 57 mbar
for acclimated pilots (paCO2 = 40 mbar) we get pAO2 ~ 70 mbar
fO2 = 1.0, pAtm = 138 mbar (2.0 psi), R= 1.0
even for extremely acclimated pilots (pACO2 ~ 36 mbar) we get pAO2 ~ 35 mbar

From this we can clearly see why pilots last only a short time at 2.0 psi pure oxygen. Even for extremely acclimated individuals it is as if they are well into the Death Zone. One would need to acclimate to low pressue for many days like Everest climbers to have any hope of significant activity. Anything less would allow one to only maintain consciousness for a short time.

Conversely, we can see why 2.5 psi of pure oxygen is acceptable for pilots. Under these conditions (depending on their level of acclimation) a pilot would feel as if they were between 10,000 and 18,000 ft, which is the range in which people can still operate fairly normally, but tire somewhat easily and aren't as capable as they are at sea level.

Now, to apply this to terraforming Mars. It's a bit cumbersome to keep playing with numbers to shift from a 21% oxygen atmosphere to a 100% one, so I made the graph below. I just took the Alveolar Gas Equation and solved for the oxygen fraction in terms of the total atmospheric pressure, then plotted out curves using the parameters for various altitudes:

Any combination of fO2 and pAtm that falls on an altitude curve will have the respiratory effects of being at that altitude on Earth. For example, if you simply drew a horizontal line at fO2 = 21% the intersection point of each altitude curve with it would indicate the atmospheric pressure at that altitude on Earth. Thus, at 21% O2 the 0 ft curve is about 1010 mbar (1 atm) and the 18,000 ft curve is just above 500 mbar (0.5 atm).

But on Mars it would be difficult (and unnecessary) to obtain a 79% backfill of nitrogen, argon, and other gases. So how much oxygen do we need to use to get the same effects as, say, 18,000 ft on Earth? Well, let's say we want a pure oxygen atmosphere, since that'd be the thinnest possible. Just follow the 18,000 ft curve up to the cut-off at the top where fO2 = 1.0 (you obviously can't have an atmosphere more than 100% oxygen). Looking down at the pAtm axis, we see that we would need a bit under 160 mbar total atmosphere. If you actually plug in the numbers, you get 156 mbar. If you plug in for pure oxygen at 20,000 ft, you get 147 mbar. Given these numbers, it's reasonable to deduce a minimum pure oxygen atmosphere of 150-160 mbar (2.2-2.3 psi) for permanant human habitation.

But we probably won't have a pure oxygen atmosphere. It'd be more realistic to have, say, a 50% oxygen atmosphere with the rest made up by nitrogen, carbon dioxide, etc. It cuts down on flammability (a complex issue by itself) and some living things need nitrogen and/or carbon dioxide in the air anyway. So, we find where the 18,000 ft curve has an fO2 value of 50% and we get a total atmospheric pressure of 250 mbar (3.6 psi), 125 mbar (1.8 psi) of which would be oxygen. If you follow the 20,000 ft curve you get a total pressure of 230 mbar (3.3 psi), 115 mbar (1.7 psi) of which is oxygen. Exactly what percentage of the atmosphere you want to be oxygen will depend on how much flammability you're willing to tolerate, as well as what other gases are present, e.g. a given partial pressure of CO2 is more flame retardant than an equal pressure of N2. And of course in real life it'll depend on what's availible.

Bacteria, algae, fungus, and lichen are crucial in kickstarting terraformation, and their contribution cannot be understated. They are the most readily suited organisms to the current (or an only slightly changed) Martian environment, and will be key in colonizing the initially rather nasty conditions with briny water and a thin, oxygen deprived atmosphere. However, we want to make the transition to more advanced lifeforms as quickly as possible. Moss and other bryophytes are the natural (in every sense of the word) second step. Once the Martian environment has been altered just enough to allow their growth outside greenhouses, they should be spread as quickly as possible to accelerate the terraformation process beyond what is possible with the "first step" lifeforms.

Even artificially iron nutrient enhanced algal blooms are incapable of approaching the sphagnum peat bog's ability to sequester carbon (and thus produce humus and an oxygen rich atmosphere). At 2 grams/m^2/yr for the algae (Buesseler & Boyd 2003) versus 14-72 grams/m^2/yr for the sphagnum (Belyea & Malmer 2004), the bog is about an order of magnitude or more efficient. Note that both these studies took place at extreme latitudes on Earth, and so are not bad analogies for Mars in some ways.

By the way, iron radicals grabbing all the oxygen will not be the limiting factor for O2 concentrations in Martian bog water. Iron depends quadratically on OH- concentraions to oxidize with dissolved O2. This means that in a typical pH 4 bog Fe+2 will oxidize to Fe+3 at a rate 1,000,000 times slower than in neutral water. In fact, ~pH 4 is considered something of a transition point at which there is so much unreacting iron and dissolved oxygen sitting around that it becomes energetically favorable as a metabolic pathway. The bacteria Thiobacillus ferrooxidans is famous for exploiting this. Another factor reducing oxygen solubility is salinity, but even in solutions 2 times as salty as Earth's ocean the O2 saturation point is reduced by less than half its pure water value. Unfortunately, it turns out that the most serious limiting factor to O2 solubility in water is the partial pressure of oxygen in the atmosphere, which means we still have to substantially raise O2 levels. It will require at least 2 mbar O2 and probably more like 10 mbar to raise solubility to the point that water at 10°C can accept the dissolved oxygen values typically found in peat bog water (Rigg et al. 1927). Colder water would require slightly less pressure and warmer water would require slightly more. Note these minimum O2 values are consistent with the >0.1 mbar lower limit that the fungus analogy provides and the "below 30 mbar" upper limit from the study that I mentioned in my last post.

A final note on protection from UV and elevated CO2. Many mosses, including some Sphagnum species, are quite capable of thriving completely submerged, provided there is sufficient dissolved CO2 (not a problem on Mars) and O2 (which must first be raised by algae or some other organism). Since a fairly thin layer of water can very effectively block the most damaging UV rays on Mars, many mosses (and other aquatic bryophytes like some hornworts and liverworts) can be protected from radiation early on when the atmosphere might not otherwise be thick enough to satisfactorily block radiation. This technique has been discussed several times before in these forums for other organisms. Another benefit of being underwater is that it limits the amount of CO2 that will reach the moss from the atmosphere. Bogs are often naturally supersaturated with CO2 formed by biological processes, and have been found at up to 6.5 mM (Nilsson & Bohlin 1993). This suggests that a submerged sphagnum bog in 10°C water could easily take a 130mbar CO2 partial pressure atmosphere, and probably much more before the moss became uncomfortable. This is remarkable considering that the experiments I mentioned in my last post determined a maximum 20 mbar CO2 partial pressure for unsubmerged moss. As with O2, an increase in temperature will lower solubility in water (here increasing the maximum CO2 pressure that a submerged bog cold take), while decreasing the temperature will raise the solubility (requiring a lower atmospheric CO2 pressure to avoid damaging the moss).

I also happen to think that mossy bogs are prettier than puddles of algae.

We need to be careful which sphagnum moss is used. I found a very interesting and somewhat sobering paper on one kind of sphagnum moss's reaction to UV-B.

Note that the paper can be taken both ways: it found that increased UV-B didn't really hurt the species of moss studied, but it also cautions that other mosses often react differently and extrapolation must be done carefully. Biodiversity is good, so we'd need to round up as many of the UV-B tolerant sphangum species as possible.

I still think that sphagnum bogs are a critical step in the terraformation of Mars. It's not widely known, but Mars DOES have a permanant ozone layer. It is formed by the breakdown of CO2 by high frequency UV. It is currently not enough to produce significant protection, but if the CO2 atmosphere were thickened and some preliminary microbial mats began pumping out a small amount of oxygen maybe it could begin to become substantial?

That's a good point noosfractal.

The subsurface temperature gradient in a locality is dependant not only on the soil's thermodynamic properties, but on the past history of that area's surface temperature. I talked about the soil before, but you've made me realize that the past history is more complex and important than I initially thought.

As I said in my analysis above, I was taking 0C to be the average annual temperature. Implicit in this is the assumption that seasonal temperature variations dominate the determination of a locality's surface temperature. However, this is not always the case.

I mentioned before that there are three time regimes that come to play in determining surface temperature: diurnal, seasonal, and geological. Which of these influences dominates depends on the situation. On Mercury, which has very little atmosphere and tilt, there are huge diurnal fluctuaions, ranging from 90 K to 700 K, and virtually no seasonal changes. On Earth the diurnal and seasonal effects are roughly equivalent at the equator, while at the poles seasonal fluctuations dominate. A similar situation would be found on Mars, except that in the midst of terraformation there would be a very pronounced 'geological' effect of global warming (much more so than on Earth).

The upshot of all this is that you will have very different subsurface temperature gradients on Mars-in-progress depending on what latitude you are at, how stable your diurnal fluctuations are (i.e. how thick your atmosphere is), and how quickly you are warming the planet. That all sounds complicated, but a first-order approximation for the subsurface gradient is actually not hard to derive given a function that describes the surface temperature history of a given area. I should probably try slapping a parametric general equation together...